Systems and methods for virtual aperature radar tracking

ABSTRACT

A system for virtual aperture array radar tracking includes a transmitter that transmits first and second probe signals; a receiver array including a first plurality of radar elements positioned along a first radar axis; and a signal processor that calculates a target range from first and second reflected probe signals, corresponds signal instances of the first reflected probe signal to physical receiver elements of the radar array, corresponds signal instances of the second reflected probe signal to virtual elements of the radar array, calculates a first target angle between a first reference vector and a first projected target vector from the first reflected probe signal, and calculates a position of the tracking target relative to the radar array from the target range and first target angle.

CROSS-REFERENCE TO RELATED APPLICATIONS

This application is a continuation of U.S. patent application Ser. No.16/032,369 filed 11 Jul. 2018, which is a continuation of U.S. patentapplication Ser. No. 15/883,372, filed on 30 Jan. 2018 (U.S. Pat. No.10,048,366 issued 14 Aug. 2018), which are incorporated in theirentirety by this reference.

TECHNICAL FIELD

This invention relates generally to the radar field, and morespecifically to new and useful systems and methods for virtual apertureradar tracking.

BACKGROUND

Traditional array-based receivers calculate azimuth and/or elevation bymeasuring the time or phase difference between received probe signals atdifferent receivers (or antennas) within the array(s), as shown in FIG.1 (1D array), using beamforming (e.g., digital beamforming). Similareffects may be produced using a transmit array instead of a receiverarray. These traditional solutions are limited: angular resolutiondepends both on the number of elements in the array and the anglebetween the array and the target:

$\theta_{resolution} \approx \frac{\lambda}{{Nd}\;\cos\;\theta}$where N is the number of elements in the array and d is the distanceseparating them.

Thus, there is a need in the radar field to create new and usefulsystems and methods for virtual aperture radar tracking. This inventionprovides such new and useful systems and methods.

BRIEF DESCRIPTION OF THE FIGURES

FIG. 1 is a prior art example diagram of a 1D receiver array radarsystem;

FIG. 2 is chart view of a method of an invention embodiment;

FIG. 3A is an example view of physical aperture in SAR tracking;

FIG. 3B is an example view of virtual aperture in SAR tracking;

FIG. 4A is an example view of a first physical aperture in VAA tracking;

FIG. 4B is an example view of a second physical aperture in VAAtracking;

FIG. 4C is an example view of a virtual aperture in VAA tracking;

FIG. 5A is a diagram view of a signal incident on a traditional receiverarray;

FIG. 5B is a signal view of a signal incident on a traditional receiverarray;

FIG. 6A is a diagram view of a signal incident on a VAA system;

FIG. 6B is a signal view of a signal incident on a VAA system;

FIG. 7 is an example view of phase shift from two transmitter elementsseparated by a distance;

FIG. 8 is a diagram view of virtual transmitter and receiver elements ina VAA system;

FIG. 9 is a Cartesian coordinate view of object position parameters;

FIG. 10 is a diagram view of a system of an invention embodiment; and

FIG. 11 is a diagram view of a system of an invention embodiment.

DESCRIPTION OF THE INVENTION EMBODIMENTS

The following description of the invention embodiments of the inventionis not intended to limit the invention to these invention embodiments,but rather to enable any person skilled in the art to make and use thisinvention.

1. Method for Virtual Aperture Array Radar Tracking

A method 100 for virtual aperture array (VAA) radar tracking includestransmitting a set of probe signals S110, receiving a set of reflectedprobe signals S120, and calculating initial tracking parameters from theset of reflected probe signals S130, as shown in FIG. 2. The method 100may additionally include refining the initial tracking parameters S140and/or modifying probe signal characteristics S150.

As discussed in the background section, traditional array-based radarsystems are limited: angular resolution depends both on the number ofelements in the receiver array and the angle between the array and thetarget:

$\theta_{resolution} \approx \frac{\lambda}{{Nd}\;\cos\;\theta}$where N is the number of elements in the array and d is the distanceseparating them.

Here, the number of array elements (and distance separating them)relates to the receiver's aperture; that is, more elements (or increasedelement spacing) results in increased receiver aperture. As the angularresolution formula makes clear, to increase angular resolution (withoutchanging carrier frequency), one must increase the receiver's aperture.Typically, this is done by adding receiver array elements or increasingthe separation distance between elements; however, these techniquesincrease either or both of the receiver array's physical size or itscost and physical complexity. Nevertheless, this traditional techniqueshines in that it increases radar resolution with relatively littlechange in processing latency.

As an alternative to this traditional technique, synthetic apertureradar (SAR) was created. In SAR, a moving antenna (or antenna array)captures multiple signals sequentially as it moves, as shown in FIG. 3A;these signals are then combined (using knowledge of the antenna'smovement) to simulate the effect of a larger antenna, as shown in FIG.3B. SAR manages to simulate increased radar aperture (thus increasingradar resolution), but requires precise antenna motion data andgenerally entails a significant increase in processing latency. Bothrequirements are problematic in many applications.

The method 100 utilizes a novel technique to simulate increased radaraperture (as SAR does) without incurring the additional cost/size ofincreasing physical array size or the heavy downsides of SAR (e.g.,motion data requirements and high processing latency). This technique isreferred to Virtual Aperture Array (VAA) radar tracking. Note that whilethe term “virtual aperture” has various uses in the field of radartracking, as used in the present application, Virtual Aperture Arrayradar tracking specifically refers to the tracking techniques describedherein (and not to any unrelated technology sharing the term).

The VAA radar tracking technique of the method 100 functions bycapturing instances of a first signal at a physical array simultaneously(like a traditional phased array), then capturing instances of a secondsignal at the same physical array (the instances of the second signalcaptured simultaneously, but not necessarily at the same time as theinstances of the first signal are captured); if applicable, capturingadditional instances in the same manner, and finally processing the datareceived from all captured instances together to generate ahigher-resolution radar tracking solution than would otherwise bepossible. Notably, the first and second signals (as well as anyadditional signals) are encoded with distinct phase information. Thisdistinct phase information enables the instances of the second signal tobe treated as being received at a virtual receiver array displaced fromthe physical array (creating a virtual aperture larger than the physicalaperture). For example, a first signal may be captured as shown in FIG.4A, having a first phase encoding, and a second signal may be capturedas shown in FIG. 4B, having a second phase encoding; these signals maybe processed together as shown in FIG. 4C.

As shown in FIG. 5A, when a reflected signal is received from a targetat an angle (i.e., not normal to) the six-element radar array, thesignal received at each receiver element in the array is phase shiftedrelative to the signal received at other elements in the array, as shownin FIG. 5B. From the phase shift and spacing between elements, the angleof the target to the array may be determined.

As shown in FIG. 6A, the method 200 can simulate the same aperture withonly three elements through the use of two phase shifted signals,resulting in the signals at receiver elements as shown in FIG. 6B (notethat the signal at RX1 at t2 is similar to the signal at RX4 in FIG. 5B,and so on). The positioning of the “virtual elements” is dependent onthe phase shift between the first and second signals.

The method 100 is preferably implemented by a system for VAA radartracking (e.g., the system 200), but may additionally or alternativelybe implemented using any suitable object tracking system capable ofperforming virtual aperture array object tracking (e.g., SONAR, LIDAR).

S110 includes transmitting a set of probe signals. S110 functions totransmit a set of signals that, after reflection by a target, canprovide information about the target (e.g., relative location, velocity,etc.). S110 preferably includes transmitting=frequency shift keyed (FSK)RADAR signals or =frequency-modified continuous wave (FMCW) RADARsignals, but S110 may include transmitting any signal satisfying theseconstraints; e.g., an electromagnetic signal (as in radio waves inRADAR, infrared/visible/UV waves in LIDAR), a sound signal (as inSONAR).

S110 preferably includes transmitting at least two distinct probesignals. The set of probe signals in S110 preferably satisfy twoconstraints: each of the set is distinct in phase (as measured from somereference point) and each of the set is distinguishable from otherothers upon reception. The distinction in phase enables the effectiveincrease of aperture (and thus of angular resolution), whiledistinguishability ensures that upon reception, signal data isappropriately processed given the distinction in phase.

S110 may accomplish phase distinction in several manners. For example,S110 may include transmitting probe signals from physically distinctantenna elements. For a target at an angle from the transmitterelements, the separation encodes an inherent phase difference (one thatis dependent on the angle!), as shown in FIG. 7. For two transmittersseparated by a distance d_(TX), the phase difference at a target at θfrom normal is approximately

${d\;\phi} = {\frac{2\;\pi}{\lambda}d_{TX}\sin\;\theta}$and the phase difference seen at the receiver is approximately the same.

As a second example, S110 may include transmitting probe signals atdifferent times from the same antenna element(s), but with differentphase information. For example, S110 may include transmitting a firstsignal from an antenna element at a first time, and then transmitting asecond phase shifted signal from the same antenna element at a secondtime. Note that this is not equivalent to the phase difference in thefirst example; the phase difference dϕ (between the first and secondsignal) seen at a target is (approximately) constant and independent ofthe target's angle. Also note that while this phase distinction resultsin the simulation of increased receiver elements, it also results in thesimulation of increased transmitter elements, as shown in FIG. 8.

The result of this is that while phase distinction is generated byantenna element separation, the size of the virtual aperture is roughlythe same for all target angles; in the explicit phase shifting example,the size of the virtual aperture is target-angle dependent. For example,in the transmitter separation case, the array shift can be written as

$d_{array} = {{d\;\phi\frac{\lambda}{2\;\pi}\frac{1}{\sin\;\theta}} = d_{TX}}$while in the explicit phase shifting case

$d_{array} = {d\;\phi\frac{\lambda}{2\;\pi}\frac{1}{\sin\;\theta}}$where dϕ is a constant (and thus d_(array) is target angle dependent).

While S110 preferably performs explicit phase shifting with a phaseshifter (i.e., a device for which phase shift is ideally independent offrequency) S110 may additionally or alternatively perform explicit phaseshifting using delay lines (or any other device for which phase shiftdepends on frequency) and/or any combination of time delays and phaseshifters.

S110 may additionally or alternatively include combining phase shiftingtechniques (e.g., using multiple transmitters separated by a distanceand phase-shifting the transmitters relative to one another).

Note that while examples are given with time-constant phase shifts, S110may additionally or alternatively include modulating phase over time, byphysically shifting transmitters (i.e., giving d_(TX) time dependence)and/or by adding phase dϕ where the phase is a function of time. Thephase of the transmitted signal over time is referred to as the phasefunction. Phase functions may be referenced to any points. For example,if first and second antenna elements (separated by a non-zero distance)produce identical first and second signals respectively, it can be saidthat the phase function of the first signal (referenced to the firsttransmitter) is identical to the phase function of the second signal(referenced to the second transmitter). However, the phase of these twosignals after reflection by a target at an angle from the transmitterarray is not seen as identical at the target (or at the receiver array).

S110 may additionally or alternatively include modulating phase withrespect to angle (e.g., by using a steerable or directional antenna andmodulating phase while sweeping the antenna, using an antenna array andmodulating phase for different elements of the array, etc.).

S110 may also accomplish signal distinguishability in any of severalmanners. As previously mentioned, one way in which S110 may enablesignal distinguishability is by time-duplexing signals (e.g.,transmitting a first frequency chirp signal with a first phase encoding,then a second signal with a second phase encoding); however, S110 mayadditionally or alternatively make signals distinguishable by frequencyduplexing signals (e.g., transmitting a first frequency chirp signalwithin a first frequency band and transmitting a second frequency chirpsignal within a second frequency band non-overlapping with the first),or by encoding the signals (e.g., using a distinct frequency modulationor amplitude modulation technique to distinguish a signal from others).S110 may additionally or alternatively accomplish signaldistinguishability in any manner.

S120 includes receiving a set of reflected probe signals. S120 functionsto receive data resulting from the reflection of the probe signaltransmitted in S110. S120 preferably includes measuring phase,magnitude, and frequency information from reflected probe signals, butS120 may additionally or alternatively include measuring any availablecharacteristics of the reflected probe signals.

S120 preferably includes measuring any data necessary to recover signalidentification information (i.e., information to determine which signalof the transmitted set the reflected probe signal corresponds to).

S130 includes calculating initial tracking parameters from the set ofreflected probe signals. S130 functions to calculate a set of trackingparameters that identify at least a position of the target relative tothe radar receiver; additionally or alternatively, tracking parametersmay include additional parameters relevant to object tracking (e.g.,target velocity, target acceleration). Note that S130 may includecalculating more tracking parameters for a given target than necessaryto achieve a position solution; for example, as described later, whileonly range, azimuth angle, and elevation angle may be necessary tocalculate object position, composite angle may also be calculated andused to refine and/or check azimuth/elevation angle calculations.

Further, while S130 primarily includes calculating tracking parametersfrom the reflected probe signals, S130 may additionally or alternativelycalculate or otherwise receive parameters relevant to object tracking(e.g., radar egomotion velocity) that are not calculated using the probesignal.

Parameters used to establish target position may be defined in anycoordinate system and base. In the present application, target positionis preferably represented in a Cartesian coordinate system with theorigin at the radar (e.g., x,y,z represents target position) or aspherical coordinate system with the same origin, wherein position isdefined by range (R), azimuth (α), and elevation (θ); alternatively,target position may be described in any manner. Note that elevation (andsimilarly azimuth) is an example of an angle between a reference vectorand a projected target vector; the projected target vector is the vectorbetween the observer (e.g., the radar) and the target, projected into areference plane (the reference plane containing the reference vector).The method 100 may include calculating any such angles.

While, as previously mentioned, any parameters relevant to objecttracking may be calculated in S130, some additional parameters that maybe calculated include target range rate (dR/dt, typically calculatedfrom Doppler data), relative target velocity (the velocity of the targetwith respect to the radar receiver), radar egomotion velocity (referredto in this application as egovelocity, the velocity of the radarreceiver relative to a stationary position). These may be related; forexample, range rate is equivalent to relative target velocity multipliedby the cosine of the looking angle between the radar and the target.

S130 may additionally or alternatively include calculating compositeangle (β, the angle between the target and the radar: β=arccos[cos α×cosθ], see also FIG. 9). While composite angle may be derived fromelevation and azimuth (or vice versa), it may also be calculated fromDoppler data. If, for example, elevation and azimuth are calculated froma first data source (e.g., phase differences between receivers in areceiver array) and composite angle is calculated from a second datasource (e.g., Doppler frequency shift and relative velocity), compositeangle can be used alongside elevation and azimuth to produce a moreaccurate solution.

S130 may include calculating tracking parameters from any suitable datasource. For example, operating on a radar system with a horizontalreceiver array, azimuth may be calculated based on phase differencesbetween the reflected probe signal seen by each receiver in the array.Likewise, elevation may be calculated in a similar manner by a verticalreceiver array (and/or elevation and azimuth may be calculated insimilar manners by a two-dimensional receiver array). Range, forexample, may be calculated based on travel time of a probe signal. Rangerate, for example, may be calculated instantaneously (e.g., usingDoppler frequency shift data) or over time (e.g., by measuring change inrange over time). Composite angle, as previously discussed, may bederived from elevation/azimuth or calculated explicitly from Dopplerdata: f_(D)≈Kν cos β;

$K = {2{\frac{f_{0}}{c}.}}$

S130 may additionally include calculating relative target velocity inany manner. For example, S130 may include determining that a target isstationary and calculating relative target velocity based on egovelocity(i.e., in this case, relative target velocity is egovelocity). A targetmay be determined as stationary in any manner; for example, byidentifying the target visually as a stationary target (e.g., a stopsign may be identified by its appearance), by identifying the target byits radar cross-section as a stationary target (e.g., a stop sign or aroad may be identified by shape or other features), by comparing Dopplerdata to other (e.g., phase) data (e.g., if the composite angle providedby Doppler data is substantially different from the composite anglederived from elevation and azimuth, that may be a moving target), by thesize of the target, or in any other manner. Likewise, egovelocity may bedetermined in any manner (e.g., a GPS receiver or IMU coupled to theposition of the radar receiver, external tracking systems, etc.). Asanother example, S130 may include receiving relative target velocityinformation based on external data; e.g., an estimate from a visualtracking system coupled to the position of the radar receiver. Relativetarget velocity information may even be provided by an external trackingsystem or the target itself (e.g., transmissions of IMU data from atarget vehicle).

To determine Doppler frequency shift, S130 may include convertingreflected signal data to the frequency domain using a Fast FourierTransform (or any other technique to convert time domain signals tofrequency domain for analysis). S130 may also improve system performanceby using a Sliding Fast Fourier transform (SFFT) or similar techniquessuch as the Sliding Discrete Fourier Transform (SDFT) and Short-timeFourier Transform (STFT). These techniques allow Fourier transforms forsuccessive samples in a sample stream to be computed with substantiallylower computational overhead, improving performance.

S130 preferably includes calculating initial tracking parameters fromtwo or more reflected probe signals by linking signal instances toreceiver elements S131 and performing beamforming across receiverelements S132.

S131 includes linking signal instances to receiver elements. S131functions to correspond signal instances received at a given receiverelement to a real or virtual receiver element. For example, a radarsystem that time-duplexes first (zero-phase) and second (phase-shifted)signals may correspond a signal instance received at a physical receiverelement either to that receiver element (if the reflected signal is thefirst signal) or to a shifted virtual receiver element (if the reflectedsignal is the second signal). Note that while in some cases thetranslation of virtual receiver elements is independent of target angle,in cases where the translation of virtual receiver elements depends upontarget angle, it may be required to preliminarily determine target anglefirst (in order to know the position of virtual receiver elements) usingone or more subsets of received signals (each subset corresponding toone of the unique transmitted signals) independently prior to using allreceived signals jointly. Alternatively stated, the virtual elements maybe described in terms of the physical elements by an element translationfunction; if this translation function is not already known (as in thecase of separated transmitters) S131 may include determining the elementtranslation function for a given target.

S132 includes performing beamforming across receiver elements. Once datahas been linked to real or virtual receiver element positions, S132functions to calculate object tracking data (e.g., target range andangle) using beamforming techniques. Beamforming techniques that may beused by S132 include but are not limited to conventional (i.e.,Bartlett) beamforming, Minimum Variance Distortionless Response (MVDR,also referred to as Capon) beamforming, Multiple Signal Classification(MUSIC) beamforming, or any other beamforming technique.

S132 preferably includes performing digital beamforming for a givenobject-tracking element array using every element (both real andvirtual) in the array, but S132 may additionally or alternatively useany subset of elements to perform angle calculations. In someembodiments, S132 may include dynamically selecting the receiverelements used to perform digital beamforming techniques (e.g., based onreceiver noise or any other relevant factor).

S140 includes refining the initial tracking parameters. S140 functionsto generate a more accurate tracking solution than that initiallycalculated by S130. In a first example implementation, S140 includesrunning a Kalman filter on Cartesian coordinates of a target generatedfrom elevation angle or azimuth angle (determined from phaseinformation), range, and composite angle, constrained by error bounds ofthe composite angle. In a second example implementation, S140 includesrunning a Kalman filter on Cartesian coordinates of a target generatedfrom elevation angle and azimuth angle (determined from phaseinformation), range, and composite angle constrained by error bounds ofthe composite angle.

S140 may additionally or alternatively include filtering, refining,and/or constraining tracking parameters in any manner.

S150 includes modifying probe signal characteristics. S150 functions tomodify characteristics of the transmitted probe signals to ensure highperformance of the radar tracking algorithm. One of the advantages ofthe method 100 is that virtual transmitter/receiver elements can beadded (and the virtual aperture expanded) or removed at will. Addingmore virtual elements increases the potential accuracy of objecttracking performed by the method 100, but also increases the latency ofobject tracking.

S150 may include modifying probe signal characteristics based on theoutput of S130; for example, if during object tracking it is detectedthat a first set of data (corresponding to an earlier-transmitted signaland real receivers, for example) and a second set of data (correspondingto a later-transmitted signal and virtual receivers) fail to convergeupon an object tracking solution within some threshold error bounds,S150 may include modifying the transmitted signal to reduce the numberof virtual elements (e.g., reducing the number of distinct phase-encodedsignals from three to two).

S150 may alternatively include modifying probe signal characteristicsbased on other data. For example, S150 may include modifying probesignal data based on radar array motion (e.g., the speed of anautomobile for a car-mounted radar); modifying transmission to increasevirtual aperture when the car is moving more slowly and modifyingtransmission to decrease virtual aperture when the car is moving morequickly.

S150 may additionally or alternatively include modifying probe signalcharacteristics (at either transmitter or receiver) in any manner.

2. System for Virtual Aperture Array Radar Tracking

A system 200 for virtual aperture array (VAA) radar tracking includes atransmitter 210, a horizontal receiver array 220, and a signal processor240, as shown in FIG. 10. The system 200 may additionally include avertical receiver array 230 and/or a velocity sensing module 250.

Further, the system 200 may include any number of virtual transmitters211 and/or virtual receiver elements 222/232, as shown in FIG. 11.

Similarly to the method 100, the system 200 utilizes VAA radar trackingto simulate increased radar aperture (as SAR does) without incurring theadditional cost/size of increasing physical array size or the heavydownsides of SAR (e.g., motion data requirements and high processinglatency).

The VAA radar tracking technique of the system 200 functions bycapturing instances of a first signal at a physical array simultaneously(like a traditional phased array), then capturing instances of a secondsignal at the same physical array (the instances of the second signalcaptured simultaneously, but not necessarily at the same time as theinstances of the first signal are captured); if applicable, capturingadditional instances in the same manner, and finally processing the datareceived from all captured instances together to generate ahigher-resolution radar tracking solution than would otherwise bepossible. Notably, the first and second signals (as well as anyadditional signals) are encoded with distinct phase information. Thisdistinct phase information enables the instances of the second signal tobe treated as being received at a virtual receiver array displaced fromthe physical array (creating a virtual aperture larger than the physicalaperture). For example, a first signal may be captured as shown in FIG.4A, having a first phase encoding, and a second signal may be capturedas shown in FIG. 4B, having a second phase encoding; these signals maybe processed together as shown in FIG. 4C.

The transmitter 210 functions to transmit a signal that, afterreflection by a target, can provide information about the target (e.g.,relative location, velocity, etc.). The transmitter 210 preferablytransmits a frequency shift keyed (FSK) RADAR signal or afrequency-modified continuous wave (FMCW) RADAR signal, but thetransmitter 210 may transmit any signal satisfying these constraints;e.g., an electromagnetic signal (as in radio waves in RADAR,infrared/visible/UV waves in LIDAR), a sound signal (as in SONAR).

The transmitter 210 preferably has a single transmitting element (e.g.,a single transmit antenna), but may additionally or alternatively havemultiple transmitting elements (e.g., as in a radar array). If thetransmitter 210 has multiple elements, these elements may include asingle transmitter paired to multiple antennas (e.g., spaced in aparticular pattern and/or with antennas coupled to phase/time delays);multiple transmitters, each paired to a single antenna; multipletransmitters paired to multiple antennas, or any other configuration.

In addition to the transmitter 210, the system 200 may additionallyinclude any number of virtual transmitters 211. As described in thesection of the method 100, virtual transmitters are created byphase-shifting the output of one or more real transmitters 210 and maycorrespond to a translated element of the transmitter 210.

The horizontal receiver array 220 functions to receive data resultingfrom the reflection of the probe signal(s) transmitted by thetransmitter 210. The horizontal receiver array 220 preferably measuresphase, magnitude, and frequency information from reflected probesignals, but the horizontal receiver array 220 may additionally oralternatively measure any available characteristics of the reflectedprobe signals.

From data received from the horizontal receiver array 220, trackingparameters relating to a tracking target may be calculated. Thehorizontal receiver array 220 is preferably used to determine azimuth(α), as shown in FIG. 9, but parameters used to establish targetposition may be defined in any coordinate system and base, and thehorizontal receiver array 220 may be used to determine any relevanttracking parameters. In the present application, target position ispreferably represented in a Cartesian coordinate system with the originat the radar (e.g., x,y,z represents target position) or a sphericalcoordinate system with the same origin, wherein position is defined byrange (R), azimuth (α), and elevation (θ); alternatively, targetposition may be described in any manner. Note that elevation (andsimilarly azimuth) is an example of an angle between a reference vectorand a projected target vector; the projected target vector is the vectorbetween the observer (e.g., the radar) and the target, projected into areference plane (the reference plane containing the reference vector).The system 100 may calculate any such angles.

The horizontal receiver array 220 includes a set of receiver elements221 arranged in a pattern; e.g., along a horizontal axis. The set ofreceiver elements 221 may include a single receiver paired to multipleantennas (e.g., spaced in a particular pattern and/or with antennascoupled to phase/time delays); multiple receivers, each paired to asingle antenna; multiple receivers paired to multiple antennas, or anyother configuration.

The horizontal receiver array 220 may additionally include any number ofvirtual receiver elements 222. As described in the section of the method100, virtual receiver elements 222 are created in response to thephase-shifting of output of one or more real transmitters 210 and maycorrespond to a translated receiver element 221 of the horizontalreceiver array 220.

The horizontal receiver array 220 preferably is used to calculate anglesfrom phase information, but may additionally or alternatively be used tocalculate angles in any manner (e.g., using horizontal component ofDoppler frequency shift).

The vertical receiver array 230 is preferably substantially similar tothe horizontal receiver array 220, except that the vertical receiverarray is arranged upon an axis not parallel to the axis of thehorizontal receiver array (e.g., a vertical axis). The vertical receiverarray 230 is preferably used to calculate elevation, but mayadditionally or alternatively be used to calculate any trackingparameters. The vertical receiver array 230 includes a number ofreceiver elements 231 and may additionally include any number of virtualreceiver elements 232. As described in the section of the method 100,virtual receiver elements 232 are created in response to thephase-shifting of output of one or more real transmitters 210 and maycorrespond to a translated receiver element 231 of the vertical receiverarray 230.

The signal processor 240 functions to calculate tracking parameters fromdata collected by the horizontal receiver array 220, the verticalreceiver array 230, and/or the velocity sensing module 250. The signalprocessor 240 preferably includes a microprocessor or microcontrollerthat calculates tracking parameters according to the method 100;additionally or alternatively, the signal processor 240 may calculatetracking parameters in any manner. The signal processor 240 mayadditionally or alternatively be used to communicate with an externalcomputer (e.g., to offload computations, receive additional data, or forany other reason). The signal processor 240 may also controlconfiguration of the components of the system 200 or any calculations oractions performed by the system 200. For example, the signal processor240 may be used to control creation and/or other parameters of virtualtransmitters or virtual array elements as described in the section ofthe method 100.

The velocity sensing module 250 functions to determine the velocity ofthe system 200 (or components of the system 200, or an object coupled tothe system 200). The velocity sensing module is preferably acommunications interface that couples to an inertial measurement unit(IMU), but may additionally or alternatively be any communicationsinterface (e.g., Wi-Fi, Ethernet, ODB-II) or sensor (accelerometer,wheel speed sensor, IMU) capable of determining a speed and/or velocity.

The methods of the preferred embodiment and variations thereof can beembodied and/or implemented at least in part as a machine configured toreceive a computer-readable medium storing computer-readableinstruction. The instructions are preferably executed bycomputer-executable components preferably integrated with a system forVAA radar tracking. The computer-readable medium can be stored on anysuitable computer-readable media such as RAMs, ROMs, flash memory,EEPROMs, optical devices (CD or DVD), hard drives, floppy drives, or anysuitable device. The computer-executable component is preferably ageneral or application specific processor, but any suitable dedicatedhardware or hardware/firmware combination device can alternatively oradditionally execute the instructions.

As a person skilled in the art will recognize from the previous detaileddescription and from the figures and claims, modifications and changescan be made to the preferred embodiments of the invention withoutdeparting from the scope of this invention defined in the followingclaims.

We claim:
 1. A system for virtual aperture array radar trackingcomprising: a transmitter that transmits a first probe signal and asecond probe signal, the first probe signal having a first phasefunction and the second probe signal having a second phase functiondifferent from the first phase function; a receiver array, comprising afirst plurality of radar elements, that receives a first reflected probesignal in response to reflection of the first probe signal by a trackingtarget, and that receives a second reflected probe signal in response toreflection of the second probe signal by the tracking target; whereinthe first plurality of radar elements comprises a first receiver elementand a second receiver element, wherein the first and second receiverelements are arranged along a first array vector; wherein the trackingtarget and radar array cooperatively define a target vector from theradar array to the tracking target; and a signal processor thatcalculates a target range based on at least one of the first or secondreflected probe signals, corresponds signal instances of the firstreflected probe signal to a set of physical receiver elements of theradar array, corresponds signal instances of the second reflected probesignal to a set of virtual elements of the radar array, calculates afirst target angle between a first reference vector and a firstprojected target vector based on the first and second reflected probesignals, and calculates a position of the tracking target relative tothe radar array based on the target range and the first target angle;wherein the first projected target vector is the projection of thetarget vector onto a first reference plane, the first reference planecontaining the first array vector and the first reference vector;wherein the set of physical receiver elements comprises the first andsecond receiver elements.
 2. The system of claim 1, wherein each radarelement of the first plurality is substantially arranged along the firstarray vector.
 3. The system of claim 1, wherein: the system defines anelement translation function; and for each physical receiver element ofthe set of physical receiver elements, the physical receiver element isassociated with a respective virtual element of the set of virtualelements, wherein the respective virtual element is displaced from thephysical receiver element based on the element translation function. 4.The system of claim 3, wherein the element translation function is aconstant vector-valued function equal to a translation vector.
 5. Thesystem of claim 4, wherein the transmitter comprises a first transmitelement and a second transmit element, wherein the second transmitelement is displaced from the first transmit element by the translationvector.
 6. The system of claim 1, wherein: the first probe signal istransmitted during a first time period; and the second probe signal istransmitted during a second time period non-overlapping with the firsttime period.
 7. The system of claim 6, wherein: the first probe signalis transmitted beginning at a first time; the second probe signal istransmitted beginning at a second time; and a difference between thefirst phase function, referenced to the first time, and the second phasefunction, referenced to the second time, varies with time.
 8. The systemof claim 1, wherein the first phase function varies with time.
 9. Thesystem of claim 1, wherein the signal processor modifies at least one ofthe first and second probe signals in response to calculated positiondata, comprising modifying the at least one of the first and secondprobe signals to add virtual elements to the radar array.
 10. The systemof claim 1, wherein: the receiver array further comprises secondplurality of radar elements, wherein the radar elements of the secondplurality are substantially arranged along a second array vectornon-parallel with the first array vector, wherein the set of physicalreceiver elements further comprises the second plurality of radarelements; the signal processor calculates a second target angle betweenthe first reference vector and a second projected target vector based onthe first reflected probe signal; wherein the second projected targetvector is the projection of the target vector onto a second referenceplane, the second reference plane containing both of the second arrayvector and the first reference vector; the signal processor calculatesthe position of the tracking target based further on the second targetangle.
 11. The system of claim 10, wherein the second plurality of radarelements comprises the first receiver element and a third receiverelement.
 12. A method for virtual aperture array radar tracking,comprising: at a transmitter of a radar array, transmitting a firstprobe signal having a first phase function; at the transmitter,transmitting a second probe signal having a second phase functiondifferent from the first phase function; in response to generation of aset of reflected signals via reflection of the first and second probesignals by a tracking target in an environment surrounding the radararray, at a receiver of the radar array, receiving the set of reflectedsignals, wherein the set of reflected signals comprises a firstreflected signal and a second reflected signal; corresponding signalinstances of the first reflected signal to a set of physical receiverelements of the radar array; corresponding signal instances of thesecond reflected signal to a set of virtual elements of the radar array;based on the set of reflected signals, determining a target range equalto a magnitude of a target vector from the radar array to the trackingtarget; based on the set of reflected signals, determining a targetangle between a first reference vector and a first projected targetvector, wherein the first projected target vector is the projection ofthe target vector onto a first reference plane, the first referenceplane containing the first reference vector and a first array vectordefined by the radar array; and based on the target range and the targetangle, determining a position of the tracking target relative to theradar array.
 13. The method of claim 12, wherein: the first reflectedsignal is generated via reflection of the first probe signal by thetracking target; and the second reflected signal is generated viareflection of the second probe signal by the tracking target.
 14. Themethod of claim 13, wherein receiving the set of reflected signalscomprises receiving the first and second reflected signals concurrently.15. The method of claim 14, wherein: the receiver comprises a firstreceiver element and a second receiver element; and receiving the firstand second reflected signals concurrently comprises: receiving the firstreflected signal at the first receiver element; and receiving the secondreflected signal at the second receiver element.
 16. The method of claim14, wherein: the transmitter comprises a first transmit element and asecond transmit element; transmitting the first probe signal isperformed at the first transmit element; and transmitting the secondprobe signal is performed at the second transmit element, wherein thefirst and second probe signals are transmitted concurrently.
 17. Themethod of claim 12, wherein: the transmitter comprises an array oftransmit elements; and the transmitter transmits the first probe signalby independently modulating the phases of each transmit element of thearray.
 18. The method of claim 17, wherein the phases of the array oftransmit elements are modulated with respect to a beam steering angle.19. The method of claim 12, wherein a difference between the first andsecond phase functions varies with time.
 20. The method of claim 12,further comprising: based on at least one of the target range or thetarget angle, determining a modified set of probe signals to add atleast one virtual element to the radar array; at the transmitter,transmitting the modified set of probe signals; in response togeneration of a second set of reflected signals via reflection of themodified set of probe signals by the tracking target, at the receiver,receiving the second set of reflected signals; based on the second setof reflected signals, determining an updated target range; based on thesecond set of reflected signals, determining an updated target angle;and based on the updated target range and the updated target angle,determining an updated position of the tracking target relative to theradar array.